I don't have the source code in a good state to publish yet but here's where I'm at. At some point before this CGO_LDFLAGS does work and the header is found (omit the -ldflags args). But when it goes to statically link it can no longer find the header.

  CGO_LDFLAGS="-L$(pwd)/duckdb/src/include" CGO_CFLAGS="-I$(pwd)/duckdb/src/include" go build -ldflags '-extldflags " -lstdc++ -lm -lduckdb -static"'
  # github.com/marcboeker/go-duckdb
  ../../go/pkg/mod/github.com/marcboeker/go-duckdb@v0.0.0-20220427142532-cd9f33e64d9a/connection.go:4:10: fatal error: duckdb.h: No such file or directory
    4 | #include <duckdb.h>
      |          ^~~~~~~~~~
  compilation terminated.

Edit, nevermind about not being in a good state! Here's my code: https://github.com/multiprocessio/duckdb-tests.